Question: What do the following two equations represent? $-4x+3y = 5$ $-4x+3y = -1$
Answer: Putting the first equation in $y = mx + b$ form gives: $-4x+3y = 5$ $3y = 4x+5$ $y = \dfrac{4}{3}x + \dfrac{5}{3}$ Putting the second equation in $y = mx + b$ form gives: $-4x+3y = -1$ $3y = 4x-1$ $y = \dfrac{4}{3}x - \dfrac{1}{3}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.